Natural systems are generally complex, consisting of a large number of interlinked/integrated components of heterogenous properties [1]}. The individual components of such complex systems have non-linear characters [2]}, [3]}. Their interaction can give rise to emergent local behaviors at different scales. These local behaviors correspond to scale dependent properties of the system [3]}. An important property of complex systems is self-organization, which can be captured by fractal (scale independent self-similar) or multifractal (scale dependent fractal) processes [5]}.
Kantelhardt et al. [6]} developed a numerical method known as the multifractal detrended fluctuation analysis (MFDFA) to calculate various multifractal parameters for characterizing multifractal scaling properties and detecting long-range correlations in noisy, non-stationary time series data of complex systems. The method is based on a generalization of the detrended fluctuation analysis (DFA) initially given by Peng et al [7]}. Gu and Zhou [8]} extended the conventional MFDFA to the two-dimensional multifractal detrended fluctuation analysis (2D-MFDFA) to analyze higher dimensional fractals and multifractals.
